There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

When a parameter space has a certain underlying structure, the ordinary gradient of a function does not represent its steepest direction, but the natural gradient does. Information geometry is used for calculating the natural gradients in the parameter space of perceptrons, the space of matrices (for blind source separation), and the space of linear dynamical systems (for blind source deconvolution). The dynamical behavior of natural gradient online learning is analyzed and is proved to be Fisher efficient, implying that it has asymptotically the same performance as the optimal batch estimation of parameters. This suggests that the plateau phenomenon, which appears in the backpropagation learning algorithm of multilayer perceptrons, might disappear or might not be so serious when the natural gradient is used. An adaptive method of updating the learning rate is proposed and analyzed.

Natural gradient works efficiently in learning

https://users.dimi.uniud.it/~antonio.dangelo/Robotica/2012/helper/leggedRobot/Ijspeert08NN.pdf

2008 Special Issue: Central pattern generators for locomotion control in animals and robots: A review

Computer and Robot Vision Vol. 1, by R.M. Haralick and Linda G. Shapiro, Addison-Wesley, 1992, ISBN 0-201-10887-1.

Computer and Robot Vision

We present a new strategy for reliable automatic classification of local seismic signals and volcano-tectonic earthquakes (vt). The method is based on a supervised neural network in which a new approach for feature extraction from short period seismic signals is applied. To reduce the number of records required for the analysis we set up a specialized neural classifier, able to distinguish two classes of signals, for each of the selected stations. The neural network architecture is a multilayer perceptron (mlp) with a single hidden layer. Spectral features of the signals and the parameterized attributes of their waveform have been used as input for this network. Feature extraction is done by using both the linear predictor coding technique for computing the spectrograms, and a function of the amplitude for characterizing waveforms. Compared to strategies that use only spectral signatures, the inclusion of properly normalized amplitude features improves the performance of the classifiers, and allows the network to better generalize. To train the mlp network we compared the performance of the quasi-Newton algorithm with the scaled conjugate gradient method. We found that the scaled conjugate gradient approach is the faster of the two, with quite equally good performance. Our method was tested on a dataset recorded by four selected stations of the Mt. Vesuvius monitoring network, for the discrimination of low magnitude vt events and transient signals caused by either artificial (quarry blasts, underwater explosions) and natural (thunder) sources. In this test application we obtained 100% correct classification for one of the possible pairs of signal types (vt versus quarry blasts). Because this method was developed independently of this particular discrimination task, it can be applied to a broad range of other applications.

/pdf/automatic-classification-of-seismic-signals-at-mt-vesuvius-u1833q6f6z.pdf

Automatic Classification of Seismic Signals at Mt. Vesuvius Volcano, Italy, Using Neural Networks

We report on the implementation of an automatic system able to discriminate between explosion-generated artificial seismic events and local earthquakes in the Phlegraean Fields (Italy). The explosions are fired weekly at the sea bottom (tens of meters below sea level) by fishermen in Pozzuoli bay; earthquakes are volcano-tectonic quakes with depths shallower than 4 km. The discrimination system is based on an artificial neural network and is composed of two modules. The first is devoted to the extraction of the seismogram signatures and the second to the classification of the seismic events into two classes. For the features extraction (preprocessing stage), instead of the conventional Fourier spectral analysis, we use a Linear Prediction Coding (LPC) algorithm. This approach compresses the data from 256 samples to only 7 parameters and can extract robust features for the spectrogram representation. The classification is performed using a supervised neural algorithm based on a Multilayer Neural Network (MLP) architecture. We applied the method to a set of 30 seismic events recorded by the stations of the local seismic network, 15 of which were generated by the fishermen's explosions and 15 were volcano-tectonic earthquakes. We dealt with a total of 280 records from different stations, 121 relating to explosions and 159 to earthquakes. Data were divided in a training set containing 120 traces for earthquakes and 90 for explosions, and a test set containing 70 traces corresponding to 39 records for earthquakes and 31 records for explosions. On the test set the neural net gave a classification performance of 92%, indicating a good ability of the net to generalize.

Manuscript received 10 January 2002.

Discrimination of Earthquakes and Underwater Explosions Using Neural Networks

In this article we report on the implementation of an automatic system for discriminating landslide seismic signals on Stromboli island (southern Italy). This is a critical point for monitoring the evolution of this volcanic island, where at the end of 2002 a violent tsunami occurred, triggered by a big landslide. We have devised a supervised neural system to discriminate among landslide, explosion-quake, and volcanic microtremor signals. We first preprocess the data to obtain a compact representation of the seismic records. Both spectral features and amplitude-versus-time information have been extracted from the data to characterize the different types of events. As a second step, we have set up a supervised classification system, trained using a subset of data (the training set) and tested on another data set (the test set) not used during the training stage. The automatic system that we have realized is able to correctly classify 99% of the events in the test set for both explosion-quake/ landslide and explosion-quake/microtremor couples of classes, 96% for landslide/ microtremor discrimination, and 97% for three-class discrimination (landslides/ explosion-quakes/microtremor). Finally, to determine the intrinsic structure of the data and to test the efficiency of our parametrization strategy, we have analyzed the preprocessed data using an unsupervised neural method. We apply this method to the entire dataset composed of landslide, microtremor, and explosion-quake signals. The unsupervised method is able to distinguish three clusters corresponding to the three classes of signals classified by the analysts, demonstrating that the parametrization technique characterizes the different classes of data appropriately.

Automatic Discrimination among Landslide, Explosion-Quake, and Microtremor Seismic Signals at Stromboli Volcano Using Neural Networks

Approximation of continuous and discontinuous mappings by a growing neural RBF-based algorithm

We have implemented a method based on an unsupervised neural network to cluster the waveforms of very-long-period (VLP) events associated with explosive activity at the Stromboli volcano (southern Italy). Stromboli has several active vents in the summit area producing together more than 200 explosions/day. We applied this method to investigate the relationship between each vent and its associated VLP explosive waveform.

We selected 147 VLP events recorded between November and December 2005, when digital infrared camera recordings were available. From a visual inspection of the infrared camera images, we classified the VLPs on the basis of which vent produced each explosion. We then applied the self-organizing map (SOM), an unsupervised neural technique widely applied in data exploratory analysis, to cluster the VLPs on the basis of their waveform similarity.

Our analysis demonstrates that the most recurrent VLP waveforms are usually generated by the same vent. Some exceptions occurred, however, in which different waveforms are associated with the same vent, as well as different vents generating similar waveforms. This suggests that the geometry of the upper conduit-vent system plays a role in shaping the recurring VLP events, whereas occasional modest changes in the source process dynamics produce the observed exceptions.

Silvia Scarpetta

Papers

Automatic Classification of Seismic Signals at Mt. Vesuvius Volcano, Italy, Using Neural Networks

Discrimination of Earthquakes and Underwater Explosions Using Neural Networks

Automatic Discrimination among Landslide, Explosion-Quake, and Microtremor Seismic Signals at Stromboli Volcano Using Neural Networks

Approximation of continuous and discontinuous mappings by a growing neural RBF-based algorithm

Unsupervised Neural Analysis of Very-Long-Period Events at Stromboli Volcano Using the Self-Organizing Maps